One of Broadway’s most powerful theater owners and producers, Jordan Roth, kicked off a raunchily comedic web video series on Thursday with a first installment that refers to Mr. Trump as “a national disgrace” and manages to allude to his combover hair style and his imagined penis size while critiquing a focus on personal appearances (“let’s take the focus off of looks and keep our insults humane”).

Mr. Roth said the series, called “The Birds and the BS,” is intended to address the cultural coarsening that has accompanied the Trump era, reminding adults of the courtesies they learned as children, but using pungent language to attract attention, both to the videos and the broader issue.

“We need a kids’ show for us, to remind ourselves of these basic human decencies in the complicated adult world that we now swim in, and if we can do that with a laugh and a catchy tune and a little bit of shock, then we might actually watch it, and then think about it,” he said.

Mr. Roth, whose company, Jujamcyn Theaters, owns five of the 41 Broadway theaters, has not been shy about his opposition to the Trump administration — he is a longtime Democratic donor who co-produced a Broadway fund-raiser for Hillary Clinton’s campaign.

But his decision to create a web series with a first episode that jabs pointedly at the president is striking because of Mr. Roth’s history with Mr. Trump. Mr. Roth’s father, Steven, a prominent real estate magnate in New York City, has been politically and financially allied with Mr. Trump.

“Yes, he was at my wedding, but when it became clear what his politics were, and what his priorities were, and what his administration would do to things I hold dear — that was the change,” Jordan Roth said.

“It’s not meant to be personal,” he added. “It’s saying something about where we are right now, and the language and the potential shock value of it is part of the point, because we are numb.”

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Senator Marco Rubio and Donald J. Trump at a debate of Republican presidential candidates on March 3, 2016. In one exchange, Mr. Trump mentioned Mr. Rubio’s taunt that Mr. Trump’s “small hands” correlated with another part of his anatomy. Mr. Trump then shot back: “I guarantee you, there’s no problem. I guarantee you.”CreditRichard Perry/The New York Times

The Roths have remained a close family even as Steven Roth, who jointly owns a skyscraper in New York and one in San Francisco with Mr. Trump, has counseled the president — he was the member of an infrastructure advisory council before it disbanded last summer — and Jordan Roth has criticized him. “We have different political opinions and beliefs, and we can talk about them, but they are not the basis of our relationship,” Jordan Roth said. “I know for some people that may be difficult to understand, but he is my father and I am his son and that matters more. I love him.”

Steven Roth did not respond to an email seeking comment on his son’s video.

Daryl Roth — Steven’s wife and Jordan’s mother — is a prominent Broadway producer who has gravitated toward progressive plays that often call attention to challenges facing women and gay people. She attended the Trump inauguration with her husband and has avoided publicly taking sides on the administration.

Ms. Roth, in an email, gave the video a positive review, calling it “hilarious, really clever and witty, and certainly timely.” “I love it,” she added. “It will definitely get people talking.”

A White House spokeswoman did not respond to a request for comment.

Jordan Roth, who has had a longtime interest in performing and has dabbled in video production previously, conceived of this new series months ago, with the idea of developing “a kids’ show for adults,” modeled on “Mister Rogers’ Neighborhood” and “Pee-wee’s Playhouse.”

“If we can take our frustration and confusion and dismay and fear and create with it, that’s what we need to do,” he said.

The video, which includes off-color language, features an animated character voiced by Billy Porter, an actor who won a Tony Award for his role in “Kinky Boots” (a show produced by Ms. Roth and housed in a theater owned by Jordan Roth). Mr. Porter’s animated avatar, shown alongside a sketch of Mr. Trump, says “even though they say he has tiny hands, they’re actually making fun of something else,” as an arrow points to the Trump image’s crotch.

But the animated Billy Porter then says there are better ways to criticize the president.

“We grown-ups should know better than to make fun of people’s appearances, even the people we hate,” Mr. Porter says. “There are far, far better, things to debase, like his flabby punctuation, comb-over obfuscation. It’s his shameful bigotries that look so dumpy in his khakis.”

In an interview, Mr. Porter said he agreed to participate as an expression of his opposition.

“It’s about the resistance,” he said. “James Baldwin says it’s the artist’s job to disturb the peace, and I take that very seriously. I’m not a community organizer, I’m not a politician, but with creative energy I can help change hearts and minds with my stuff.”

Mr. Porter has also made his own video, reinterpreting the Rodgers and Hammerstein standard “I’m Gonna Wash That Man Right Outta My Hair” as a form of opposition to the Trump administration. He said the tone of the videos is in keeping with the tone of the moment.

“I thought it has to be as irreverent as he is,” he said. “There’s no pulling any punches any more. Yes, it’s on the nose, but that’s where we are, so let’s vomit it all out there.”

Mr. Roth said he hopes to introduce a new video every other week, focused on current affairs and “how we talk to each other, behave toward each other, and care for each other, or not — the big stuff.”